Feature engineering for electricity load forecasting

The purpose of this notebook is to demonstrate how to use skrub and polars to perform feature engineering for electricity load forecasting.

We will build a set of features from different sources:

• Historical weather data for 10 medium to large urban areas in France;

• Holidays and calendar features for France;

• Historical electricity load data for the whole of France.

All these data sources cover a time range from March 23, 2021 to May 31, 2025.

Since our maximum forecasting horizon is 24 hours, we consider that the future weather data is known at a chosen prediction time. Similarly, the holidays and calendar features are known at prediction time for any point in the future.

Therefore, features derived from the weather and calendar data can be used to engineer “future covariates”. Since the load data is our prediction target, we will can also use it to engineer “past covariates” such as lagged features and rolling aggregations.

Environment setup

We need to install some extra dependencies for this notebook if needed (when running jupyterlite). We need the development version of skrub to be able to use the skrub expressions.

%pip install -q https://pypi.anaconda.org/ogrisel/simple/polars/1.24.0/polars-1.24.0-cp39-abi3-emscripten_3_1_58_wasm32.whl
%pip install -q altair holidays https://pypi.anaconda.org/ogrisel/simple/skrub/0.6.dev0/skrub-0.6.dev0-py3-none-any.whl

ERROR: polars-1.24.0-cp39-abi3-emscripten_3_1_58_wasm32.whl is not a supported wheel on this platform.

Note: you may need to restart the kernel to use updated packages.

Note: you may need to restart the kernel to use updated packages.

# The following 3 imports are only needed to workaround some limitations
# when using polars in a pyodide/jupyterlite notebook.
import tzdata  # noqa: F401
import pandas as pd
from pyarrow.parquet import read_table

import polars as pl
import skrub
from pathlib import Path
import holidays
import warnings

# Ignore warnings from pkg_resources triggered by Python 3.13's multiprocessing.
warnings.filterwarnings("ignore", category=UserWarning, module="pkg_resources")

Time range

Let’s define a hourly time range from March 23, 2021 to May 31, 2025 that will be used to join the electricity load data and the weather data. The time range is in UTC timezone to avoid any ambiguity when joining with the weather data that is also in UTC.

We wrap the polars dataframe in a skrub variable to benefit from the built-in TableReport display in the notebook. Using the skrub expression system will also be useful later.

time_range_start = pl.datetime(2021, 3, 23, hour=0, time_zone="UTC")
time_range_end = pl.datetime(2025, 5, 31, hour=23, time_zone="UTC")
time = skrub.var(
    "time",
    pl.DataFrame().with_columns(
        pl.datetime_range(
            start=time_range_start,
            end=time_range_end,
            time_zone="UTC",
            interval="1h",
        ).alias("time"),
    ),
)
time

<Var 'time'>

Show graph

Result:

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To avoid network issues when running this notebook, the necessary data files have already been downloaded and saved in the datasets folder. See the README.md file for instructions to download the data manually if you want to re-run this notebook with more recent data.

data_source_folder = Path("../datasets")
for data_file in sorted(data_source_folder.iterdir()):
    print(data_file)

../datasets/README.md
../datasets/Total Load - Day Ahead _ Actual_202101010000-202201010000.csv
../datasets/Total Load - Day Ahead _ Actual_202201010000-202301010000.csv
../datasets/Total Load - Day Ahead _ Actual_202301010000-202401010000.csv
../datasets/Total Load - Day Ahead _ Actual_202401010000-202501010000.csv
../datasets/Total Load - Day Ahead _ Actual_202501010000-202601010000.csv
../datasets/weather_bayonne.parquet
../datasets/weather_brest.parquet
../datasets/weather_lille.parquet
../datasets/weather_limoges.parquet
../datasets/weather_lyon.parquet
../datasets/weather_marseille.parquet
../datasets/weather_nantes.parquet
../datasets/weather_paris.parquet
../datasets/weather_strasbourg.parquet
../datasets/weather_toulouse.parquet

List of 10 medium to large urban areas to approximately cover most regions in France with a slight focus on most populated regions that are likely to drive electricity demand.

city_names = [
    "paris",
    "lyon",
    "marseille",
    "toulouse",
    "lille",
    "limoges",
    "nantes",
    "strasbourg",
    "brest",
    "bayonne",
]

all_city_weather_raw = {}
for city_name in city_names:
    # all_city_weather_raw[city_name] = skrub.var(
    # f"{city_name}_weather_raw",
    all_city_weather_raw[city_name] = (
        pl.from_arrow(read_table(f"../datasets/weather_{city_name}.parquet"))
    ).with_columns(
        [
            pl.col("time").dt.cast_time_unit(
                "us"
            ),  # Ensure time column has the same type
        ]
    )

all_city_weather_raw["brest"]

shape: (38_688, 7)

time	temperature_2m	precipitation	wind_speed_10m	cloud_cover	soil_moisture_1_to_3cm	relative_humidity_2m
datetime[μs, UTC]	f32	f32	f32	f32	f32	f32
2021-01-01 00:00:00 UTC	null	null	null	null	null	null
2021-01-01 01:00:00 UTC	null	null	null	null	null	null
2021-01-01 02:00:00 UTC	null	null	null	null	null	null
2021-01-01 03:00:00 UTC	null	null	null	null	null	null
2021-01-01 04:00:00 UTC	null	null	null	null	null	null
…	…	…	…	…	…	…
2025-05-31 19:00:00 UTC	17.5175	0.0	12.0694	5.0	0.168	73.0
2025-05-31 20:00:00 UTC	16.2675	0.0	9.114471	99.0	0.168	77.0
2025-05-31 21:00:00 UTC	15.5175	0.0	7.559999	93.0	0.169	84.0
2025-05-31 22:00:00 UTC	15.5675	0.0	9.0	100.0	0.17	82.0
2025-05-31 23:00:00 UTC	15.5675	0.0	5.506941	100.0	0.171	81.0

all_city_weather_raw["brest"].drop_nulls(subset=["temperature_2m"])

shape: (36_744, 7)

time	temperature_2m	precipitation	wind_speed_10m	cloud_cover	soil_moisture_1_to_3cm	relative_humidity_2m
datetime[μs, UTC]	f32	f32	f32	f32	f32	f32
2021-03-23 00:00:00 UTC	4.628	null	10.086427	null	null	94.0
2021-03-23 01:00:00 UTC	5.028	0.0	11.183201	6.0	null	95.0
2021-03-23 02:00:00 UTC	5.078	0.0	10.966713	6.0	null	94.0
2021-03-23 03:00:00 UTC	4.628	0.0	10.464797	5.0	null	93.0
2021-03-23 04:00:00 UTC	4.428	0.0	10.464797	5.0	null	92.0
…	…	…	…	…	…	…
2025-05-31 19:00:00 UTC	17.5175	0.0	12.0694	5.0	0.168	73.0
2025-05-31 20:00:00 UTC	16.2675	0.0	9.114471	99.0	0.168	77.0
2025-05-31 21:00:00 UTC	15.5175	0.0	7.559999	93.0	0.169	84.0
2025-05-31 22:00:00 UTC	15.5675	0.0	9.0	100.0	0.17	82.0
2025-05-31 23:00:00 UTC	15.5675	0.0	5.506941	100.0	0.171	81.0

all_city_weather = time.skb.eval()
for city_name, city_weather_raw in all_city_weather_raw.items():
    all_city_weather = all_city_weather.join(
        city_weather_raw.rename(lambda x: x if x == "time" else x + "_" + city_name),
        on="time",
        how="inner",
    )

all_city_weather = skrub.var(
    "all_city_weather",
    all_city_weather,
)
all_city_weather

<Var 'all_city_weather'>

Show graph

Result:

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Calendar and holidays features

We leverage the holidays package to enrich the time range with some calendar features such as public holidays in France. We also add some features that are useful for time series forecasting such as the day of the week, the day of the year, and the hour of the day.

Note that the holidays package requires us to extract the date for the French timezone.

Similarly for the calendar features: all the time features are extracted from the time in the French timezone.

holidays_fr = holidays.country_holidays("FR", years=range(2019, 2026))

fr_time = pl.col("time").dt.convert_time_zone("Europe/Paris")
calendar = time.with_columns(
    [
        fr_time.dt.date().is_in(holidays_fr.keys()).alias("is_holiday_fr"),
        fr_time.dt.weekday().alias("day_of_week_fr"),
        fr_time.dt.ordinal_day().alias("day_of_year_fr"),
        fr_time.dt.hour().alias("hour_of_day_fr"),
    ],
)
calendar

<CallMethod 'with_columns'>

Show graph

Result:

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Electricity load data

Finally we load the electricity load data. This data will both be used as a target variable but also to craft some lagged and window-aggregated features.

load_data_files = [
    data_file
    for data_file in sorted(data_source_folder.iterdir())
    if data_file.name.startswith("Total Load - Day Ahead")
    and data_file.name.endswith(".csv")
]

electricity_raw = skrub.var(
    "electricity_raw",
    pl.concat(
        [
            pl.from_pandas(pd.read_csv(data_file, na_values=["N/A", "-"])).drop(
                ["Day-ahead Total Load Forecast [MW] - BZN|FR"]
            )
            for data_file in load_data_files
        ],
        how="vertical",
    ),
)
electricity_raw

<Var 'electricity_raw'>

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Result:

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electricity = (
    electricity_raw.with_columns(
        [
            pl.col("Time (UTC)")
            .str.split(by=" - ")
            .list.first()
            .str.to_datetime("%d.%m.%Y %H:%M", time_zone="UTC")
            .alias("time"),
        ]
    )
    .drop(["Time (UTC)"])
    .rename({"Actual Total Load [MW] - BZN|FR": "load_mw"})
    .filter(pl.col("time").dt.minute().eq(0))
    .filter(pl.col("time") >= time_range_start)
    .filter(pl.col("time") <= time_range_end)
    .select(["time", "load_mw"])
)
electricity

<CallMethod 'select'>

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Result:

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electricity.filter(pl.col("load_mw").is_null())

<CallMethod 'filter'>

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Result:

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electricity.filter(
    (pl.col("time") > pl.datetime(2021, 10, 30, hour=10, time_zone="UTC"))
    & (pl.col("time") < pl.datetime(2021, 10, 31, hour=10, time_zone="UTC"))
).skb.eval().plot.line(x="time:T", y="load_mw:Q")

electricity = electricity.with_columns([pl.col("load_mw").interpolate()])
electricity.filter(
    (pl.col("time") > pl.datetime(2021, 10, 30, hour=10, time_zone="UTC"))
    & (pl.col("time") < pl.datetime(2021, 10, 31, hour=10, time_zone="UTC"))
).skb.eval().plot.line(x="time:T", y="load_mw:Q")

Check that the number of rows matches our expectations based on the number of hours that separate the first and the last dates. We can do that by joining with the time range dataframe and checking that the number of rows stays the same.

assert (
    time.join(electricity, on="time", how="inner").shape[0] == time.shape[0]
).skb.eval()

Lagged features

We can now create some lagged features from the electricity load data.

We will create 3 hourly lagged features, 1 daily lagged feature, and 1 weekly lagged feature. We will also create a rolling median and inter-quartile feature over the last 24 hours and over the last 7 days.

def iqr(col, *, window_size: int):
    """Inter-quartile range (IQR) of a column."""
    return col.rolling_quantile(0.75, window_size=window_size) - col.rolling_quantile(
        0.25, window_size=window_size
    )


electricity_lagged = electricity.with_columns(
    [pl.col("load_mw").shift(i).alias(f"load_mw_lag_{i}h") for i in range(1, 4)]
    + [
        pl.col("load_mw").shift(24).alias("load_mw_lag_1d"),
        pl.col("load_mw").shift(24 * 7).alias("load_mw_lag_1w"),
        pl.col("load_mw")
        .rolling_median(window_size=24)
        .alias("load_mw_rolling_median_24h"),
        pl.col("load_mw")
        .rolling_median(window_size=24 * 7)
        .alias("load_mw_rolling_median_7d"),
        iqr(pl.col("load_mw"), window_size=24).alias("load_mw_iqr_24h"),
        iqr(pl.col("load_mw"), window_size=24 * 7).alias("load_mw_iqr_7d"),
    ],
)
electricity_lagged

<CallMethod 'with_columns'>

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Result:

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import altair


altair.Chart(electricity_lagged.tail(100).skb.eval()).transform_fold(
    [
        "load_mw",
        "load_mw_lag_1h",
        "load_mw_lag_2h",
        "load_mw_lag_3h",
        "load_mw_lag_1d",
        "load_mw_lag_1w",
        "load_mw_rolling_median_24h",
        "load_mw_rolling_median_7d",
        "load_mw_iqr_24h",
        "load_mw_iqr_7d",
    ],
    as_=["key", "load_mw"],
).mark_line(tooltip=True).encode(x="time:T", y="load_mw:Q", color="key:N").interactive()

Investigating outliers in the lagged features

Let’s use the skrub.TableReport tool to look at the plots of the marginal distribution of the lagged features.

from skrub import TableReport

TableReport(electricity_lagged.skb.eval())

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Let’s extract the dates where the inter-quartile range of the load is greater than 15,000 MW.

electricity_lagged.filter(pl.col("load_mw_iqr_7d") > 15_000)[
    "time"
].dt.date().unique().sort().to_list().skb.eval()

[datetime.date(2021, 12, 26),
 datetime.date(2021, 12, 27),
 datetime.date(2021, 12, 28),
 datetime.date(2022, 1, 7),
 datetime.date(2022, 1, 8),
 datetime.date(2023, 1, 19),
 datetime.date(2023, 1, 20),
 datetime.date(2023, 1, 21),
 datetime.date(2024, 1, 10),
 datetime.date(2024, 1, 11),
 datetime.date(2024, 1, 12),
 datetime.date(2024, 1, 13)]

We observe 3 date ranges with high inter-quartile range. Let’s plot the electricity load and the lagged features for the first data range along with the weather data for Paris.

altair.Chart(
    electricity_lagged.filter(
        (pl.col("time") > pl.datetime(2021, 12, 1, time_zone="UTC"))
        & (pl.col("time") < pl.datetime(2021, 12, 31, time_zone="UTC"))
    ).skb.eval()
).transform_fold(
    [
        "load_mw",
        "load_mw_iqr_7d",
    ],
).mark_line(
    tooltip=True
).encode(
    x="time:T", y="value:Q", color="key:N"
).interactive()

altair.Chart(
    all_city_weather.filter(
        (pl.col("time") > pl.datetime(2021, 12, 1, time_zone="UTC"))
        & (pl.col("time") < pl.datetime(2021, 12, 31, time_zone="UTC"))
    ).skb.eval()
).transform_fold(
    [f"temperature_2m_{city_name}" for city_name in city_names],
).mark_line(
    tooltip=True
).encode(
    x="time:T", y="value:Q", color="key:N"
).interactive()

Based on the plots above, we can see that the electricity load was high just before the Christmas holidays due to low temperatures. Then the load suddenly dropped because temperatures went higher right at the start of the end-of-year holidays.

So those outliers do not seem to be caused to a data quality issue but rather due to a real change in the electricity load demand. We could conduct similar analysis for the other date ranges with high inter-quartile range but we will skip that for now.

If we had observed significant data quality issues over extended periods of time could have been addressed by removing the corresponding rows from the dataset. However, this would make the lagged and windowing feature engineering challenging to reimplement correctly. A better approach would be to keep a contiguous dataset assign 0 weights to the affected rows when fitting or evaluating the trained models via the use of the sample_weight parameter.

Final dataset

We now assemble the dataset that will be used to train and evaluate the forecasting models via backtesting.

prediction_time = time = skrub.var(
    "prediction_time",
    pl.DataFrame().with_columns(
        pl.datetime_range(
            start=time_range_start + pl.duration(days=7),
            end=time_range_end - pl.duration(hours=24),
            time_zone="UTC",
            interval="1h",
        ).alias("prediction_time"),
    ),
)
prediction_time

<Var 'prediction_time'>

Show graph

Result:

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features = (
    (
        prediction_time.join(
            electricity_lagged, left_on="prediction_time", right_on="time"
        )
        .join(all_city_weather, left_on="prediction_time", right_on="time")
        .join(calendar, left_on="prediction_time", right_on="time")
    )
    .drop("prediction_time")
    .skb.mark_as_X()
)
features

<CallMethod 'drop'>

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Result:

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horizons = range(1, 3)  # Forecasting horizons from 1 to 24 hours
target_column_name_pattern = "load_mw_horizon_{horizon}h"

targets = prediction_time.join(
    electricity.with_columns(
        [
            pl.col("load_mw")
            .shift(-h)
            .alias(target_column_name_pattern.format(horizon=h))
            for h in horizons
        ]
    ),
    left_on="prediction_time",
    right_on="time",
)

horizon_of_interest = 2
target_column_name = target_column_name_pattern.format(horizon=horizon_of_interest)
predicted_target_column_name = "predicted_" + target_column_name
target = targets[target_column_name].skb.mark_as_y()

from sklearn.ensemble import HistGradientBoostingRegressor


predictions = features.skb.apply(
    HistGradientBoostingRegressor(
        random_state=0,
        learning_rate=skrub.choose_float(
            0.01, 0.9, default=0.1, log=True, name="learning_rate"
        ),
        max_leaf_nodes=skrub.choose_int(
            3, 300, default=30, log=True, name="max_leaf_nodes"
        ),
    ),
    y=target,
)
predictions

<Apply HistGradientBoostingRegressor>

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Result:

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altair.Chart(
    pl.concat(
        [
            targets.skb.eval(),
            predictions.rename(
                {target_column_name: predicted_target_column_name}
            ).skb.eval(),
        ],
        how="horizontal",
    ).tail(24 * 7)
).transform_fold(
    [target_column_name, predicted_target_column_name],
).mark_line(
    tooltip=True
).encode(
    x="prediction_time:T", y="value:Q", color="key:N"
).interactive()

from sklearn.model_selection import TimeSeriesSplit
from sklearn.metrics import make_scorer, mean_absolute_percentage_error, get_scorer

mape_scorer = make_scorer(mean_absolute_percentage_error)

ts_cv_5 = TimeSeriesSplit(n_splits=5, max_train_size=10_000, gap=24)

predictions.skb.cross_validate(
    cv=ts_cv_5,
    scoring={
        "r2": get_scorer("r2"),
        "mape": mape_scorer,
    },
    return_train_score=True,
    verbose=1,
    n_jobs=-1,
).round(3)

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.

[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    5.3s finished

	fit_time	score_time	test_r2	train_r2	test_mape	train_mape
0	1.078	0.067	0.970	0.997	0.021	0.008
1	1.362	0.066	0.983	0.996	0.020	0.010
2	1.420	0.063	0.972	0.995	0.025	0.010
3	1.355	0.046	0.973	0.994	0.023	0.012
4	1.019	0.038	0.977	0.993	0.023	0.014

ts_cv_3 = TimeSeriesSplit(n_splits=3, max_train_size=10_000, gap=24)
randomized_search = predictions.skb.get_randomized_search(
    cv=ts_cv_3,
    scoring="r2",
    n_iter=30,
    fitted=True,
    verbose=1,
    n_jobs=-1,
)
randomized_search.results_

Fitting 3 folds for each of 30 candidates, totalling 90 fits

	learning_rate	max_leaf_nodes	mean_test_score
0	0.083669	125	0.979895
1	0.099978	114	0.979881
2	0.102284	106	0.979879
3	0.062306	120	0.979814
4	0.181067	48	0.979341
5	0.143892	52	0.979323
6	0.166852	160	0.979101
7	0.154221	23	0.978817
8	0.182366	23	0.978629
9	0.209233	79	0.978625
10	0.145675	15	0.978618
11	0.045683	29	0.976304
12	0.045739	28	0.976112
13	0.043920	26	0.975452
14	0.108023	7	0.975073
15	0.186027	5	0.974545
16	0.075361	8	0.973783
17	0.428505	274	0.972769
18	0.043979	16	0.971709
19	0.605373	3	0.970831
20	0.554965	73	0.969408
21	0.567547	14	0.968767
22	0.657843	22	0.965076
23	0.166677	3	0.964651
24	0.024859	41	0.961750
25	0.024385	9	0.931607
26	0.013570	41	0.886821
27	0.011113	50	0.843874
28	0.010402	155	0.839067
29	0.010022	11	0.773816

randomized_search.plot_results()

# nested_cv_results = skrub.cross_validate(
#     environment=predictions.skb.get_data(),
#     pipeline=randomized_search,
#     cv=ts_cv_5,
#     scoring={
#         "r2": get_scorer("r2"),
#         "mape": mape_scorer,
#     },
#     n_jobs=-1,
#     return_pipeline=True,
# ).round(3)
# nested_cv_results

# for outer_cv_idx in range(len(nested_cv_results)):
#     print(
#         nested_cv_results.loc[outer_cv_idx, "pipeline"]
#         .results_.loc[0]
#         .round(3)
#         .to_dict()
#     )

# from joblib import Parallel, delayed

# cv_predictions = []
# for ts_cv_train_idx, ts_cv_test_idx in ts_cv_5.split(prediction_time.skb.eval()):
#     features[ts_cv_train_idx].fit

predictions = features.skb.apply(
    skrub.SelectCols(
        cols=skrub.choose_from(
            [
                skrub.selectors.all(),
                skrub.selectors.filter_names(
                    lambda name: name.startswith("load_mw_"),
                ),
                skrub.selectors.filter_names(
                    lambda name: name.startswith("load_mw_")
                    or name.startswith("temperature_"),
                ),
                skrub.selectors.filter_names(
                    lambda name: name.startswith("load_mw_")
                    or name.startswith("precipitation_"),
                ),
                skrub.selectors.filter_names(
                    lambda name: name.startswith("load_mw_")
                    or name.startswith("wind_speed_"),
                ),
                skrub.selectors.filter_names(
                    lambda name: name.startswith("load_mw_")
                    or name.startswith("cloud_cover_"),
                ),
                # calendar features
                skrub.selectors.filter_names(
                    lambda name: name.startswith("load_mw_") or name.endswith("_fr"),
                ),
            ],
            name="feature_subset",
        )
    )
).skb.apply(
    HistGradientBoostingRegressor(
        random_state=0,
        learning_rate=skrub.choose_float(
            0.01, 0.9, default=0.1, log=True, name="learning_rate"
        ),
    ),
    y=target,
)

randomized_search = predictions.skb.get_randomized_search(
    cv=ts_cv_3,
    scoring="r2",
    n_iter=30,
    fitted=True,
    verbose=1,
    n_jobs=-1,
)
randomized_search.results_

Fitting 3 folds for each of 30 candidates, totalling 90 fits

	feature_subset	learning_rate	mean_test_score
0	all()	0.421860	0.973531
1	all()	0.527109	0.970536
2	filter_names(<lambda>)	0.050895	0.967113
3	all()	0.022176	0.950753
4	all()	0.016238	0.914446
5	filter_names(<lambda>)	0.092640	0.902368
6	filter_names(<lambda>)	0.056173	0.901565
7	filter_names(<lambda>)	0.250288	0.901197
8	filter_names(<lambda>)	0.246938	0.900822
9	filter_names(<lambda>)	0.133044	0.899432
10	filter_names(<lambda>)	0.061956	0.898828
11	filter_names(<lambda>)	0.072343	0.898814
12	filter_names(<lambda>)	0.048933	0.898446
13	filter_names(<lambda>)	0.185204	0.898352
14	filter_names(<lambda>)	0.038839	0.898170
15	filter_names(<lambda>)	0.133168	0.898109
16	filter_names(<lambda>)	0.108022	0.897175
17	filter_names(<lambda>)	0.231770	0.892186
18	filter_names(<lambda>)	0.370398	0.888501
19	filter_names(<lambda>)	0.338525	0.886686
20	filter_names(<lambda>)	0.393252	0.882222
21	filter_names(<lambda>)	0.427745	0.876935
22	filter_names(<lambda>)	0.020614	0.873283
23	filter_names(<lambda>)	0.566620	0.872569
24	filter_names(<lambda>)	0.018930	0.864310
25	filter_names(<lambda>)	0.015894	0.846732
26	filter_names(<lambda>)	0.015621	0.841659
27	filter_names(<lambda>)	0.841221	0.826975
28	filter_names(<lambda>)	0.012842	0.805733
29	filter_names(<lambda>)	0.010676	0.764262

# nested_cv_results = skrub.cross_validate(
#     environment=predictions.skb.get_data(),
#     pipeline=randomized_search,
#     cv=ts_cv_5,
#     scoring={
#         "r2": get_scorer("r2"),
#         "mape": mape_scorer,
#     },
#     n_jobs=-1,
#     return_pipeline=True,
# ).round(3)
# nested_cv_results

from sklearn.multioutput import MultiOutputRegressor

model = MultiOutputRegressor(
    estimator=HistGradientBoostingRegressor(
        random_state=0,
        learning_rate=skrub.choose_float(
            0.01, 0.9, default=0.1, log=True, name="learning_rate"
        ),
    ),
)

predictions = features.skb.apply(
    model, y=targets.skb.drop(cols=["prediction_time", "load_mw"]).skb.mark_as_y()
).skb.set_name("model")

from sklearn.metrics import r2_score


def multioutput_scorer(regressor, X, y, score_func, score_name):
    y_pred = regressor.predict(X)
    return {
        f"{score_name}_horizon_{h}h": score
        for h, score in enumerate(
            score_func(y, y_pred, multioutput="raw_values"), start=1
        )
    }


def scoring(regressor, X, y):
    return {
        **multioutput_scorer(regressor, X, y, mean_absolute_percentage_error, "mape"),
        **multioutput_scorer(regressor, X, y, r2_score, "r2"),
    }


predictions.skb.cross_validate(
    cv=ts_cv_5,
    scoring=scoring,
    return_train_score=True,
    verbose=1,
    n_jobs=-1,
).round(3)

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.

[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    5.3s finished

	fit_time	score_time	test_mape_horizon_1h	train_mape_horizon_1h	test_mape_horizon_2h	train_mape_horizon_2h	test_r2_horizon_1h	train_r2_horizon_1h	test_r2_horizon_2h	train_r2_horizon_2h
0	2.156	0.237	0.013	0.006	0.020	0.008	0.988	0.998	0.974	0.997
1	2.757	0.233	0.012	0.007	0.020	0.010	0.993	0.998	0.983	0.996
2	2.858	0.227	0.016	0.007	0.025	0.010	0.987	0.998	0.973	0.995
3	2.753	0.227	0.015	0.009	0.023	0.012	0.988	0.997	0.973	0.995
4	2.030	0.133	0.014	0.009	0.023	0.013	0.991	0.997	0.977	0.993

learner = predictions.skb.get_pipeline(fitted=True)

sklearn_learner = learner.find_fitted_estimator("model")
sklearn_learner.estimators_

[HistGradientBoostingRegressor(random_state=0),
 HistGradientBoostingRegressor(random_state=0)]

target_column_names = [target_column_name_pattern.format(horizon=h) for h in horizons]
predicted_target_column_names = [
    f"predicted_{target_column_name}" for target_column_name in target_column_names
]

altair.Chart(
    pl.concat(
        [
            targets.skb.eval(),
            predictions.rename(
                {
                    target_name: predicted_name
                    for target_name, predicted_name in zip(
                        target_column_names, predicted_target_column_names
                    )
                }
            ).skb.eval(),
        ],
        how="horizontal",
    ).tail(24 * 7)
).transform_fold(
    ["load_mw"] + predicted_target_column_names,
).mark_line(
    tooltip=True
).encode(
    x="prediction_time:T", y="value:Q", color="key:N"
).interactive()